1. Information Sources and Signals
Asst. Prof. Chaiporn Jaikaeo, Ph.D.
Computer Engineering Department
Kasetsart University, Bangkok, Thailand
Adapted from the notes by Lami Kaya,
© 2009 Pearson Education Inc., Upper Saddle River, NJ. All rights reserved.

2. Analog vs. Digital Data Analog data Digital data
Data take on continuous values
E.g., human voice, your weights, temperature reading
Numerical representation: real numbers
Digital data
Data take on discrete values
E.g., number of students in class, text data
Numerical representation: integers

3. Analog vs. Digital Signals
To be transmitted, data must be transformed to electromagnetic signals
Analog signals
have an infinite number of values in a range
Digital signals
Have a limited number of values

4. Data and Signals Analog Data Analog Signal Digital Data Analog Signal
Telephone
Analog Data
Analog Signal
Modem
Digital Data
Analog Signal
Codec
Analog Data
Digital Signal
Digital Transmitter/
Line Coder
Digital Data
Digital Signal

5. x(t) = x(t+T) - < t < 
Periodic Signals
A periodic signal completes a pattern within a timeframe, called a period
A signal x(t) is periodic if and only if
x(t) = x(t+T) - < t < 
value
period
time

6. Sine Waves Simplest form of periodic signal
General form: x(t) = A×sin(2ft + )
period T = 1/f
peak amplitude
time
signal strength
phase / phase shift

7. Sine Signal Characteristics
Frequency ( f ):
the number of oscillations per unit time (usually seconds)
Amplitude ( A ):
the difference between the maximum and minimum signal heights
Phase (  ):
how far the start of the sine wave is shifted from a reference time 7

8. Varying Sine Waves A = 1, f = 1,  = 0 A = 2, f = 1,  = 0

9. Sine Signal Characteristics
The frequency can be calculated as the inverse of the time required for one cycle, which is known as the period
Examples:
period T = 1 seconds
 frequency is 1 / T or 1 Hertz
period T = 0.5 seconds
 frequency is 2 Hertz 9

10. Time and Frequency Units

11. Composite Signals
Consider the signal + =

12. Composite Signals A mathematician named Fourier discovered that
Joseph Fourier ( )
Composite Signals
A mathematician named Fourier discovered that
It is possible to decompose a composite signal into series of sine functions
Each with different frequency, amplitude, and phase = +

13. Time vs. Frequency Domains1 -1 2 4
time
signal level 1 -1 2 4
signal level
frequency
Time Domain Representation
 plots amplitude as a function of time
Frequency Domain Representation
 plots each sine wave’s peak amplitude against its frequency
Frequency domain representation is much easier for analysis

14. Bandwidth of Signal
Bandwidth of a signal is the difference between the highest and lowest frequencies of the signal 14

15. Digital Signals and Signal Levels
Two-level signal
Each level represents 1 bit
Four-level signal
Each level represents 2 bits 15

16. Example
How many different levels are required if we want each level to represent n bits?

17. Baud and Bit Rate Baud  How many times a signal changes per second
Bit rate  How many bits can be sent per time unit (usually per second)
Bit rate is controlled by baud and number of signal levels
1 sec 1 00 11 10 01
1 sec
Baud = 10
Bit rate = 10 bps
Baud = 10
Bit rate = 20 bps

18. Baud and Bit Rate
Relationship between baud, signal levels, and bit rate is:
Example:
What is the bit rate (in bps) of a 16-level signal transmitted at 20 baud

19. Transmission Latency Composed of Propagation time Transmission time
Queuing time
Processing time
Entire
message
propagation
time
transmission
time

20. Transmission Latency Sender Receiver First bit leaves Data bits
Propagation time
First bit arrives
Transmission time
Last bit leaves
Last bit arrives
Time
Time

21. Fourier Analysis of Digital Signals
Digital signals consist of infinite set of sine waves
What is the bandwidth? + + +
+ …

22. Bandwidth of a Medium Most transmission media have bandwidth limit f f1
(low-pass channel)
gain
freq f0
3f0
5f0
7f0
...
9f0 f f0
3f0
5f0 f
Transmission medium t t

23. Line Coding The process of encoding digital data into digital signal
Example: Manchester encoding (used in Ethernet LAN)

24. Synchronization
The electronics at both ends of a medium must have circuitry to measure time precisely
Easy at low bit rate
Much more difficult at high bit rate

25. Synchronization
Good line coding schemes allow receiver to synchronize its timing to match the sender's 1 1 1 1 1 1 1
Bad
Good

26. Line Coding Schemes

27. Converting Analog to Digital
Common technique: Pulse Code Modulation (PCM)

28. PCM: Sampling and Quantizing
quantizing (rounding to nearest integer)
Sampling points

29. PCM: The Whole Picture *
*PAM: Pulse Amplitude Modulation

30. Minimum Sampling Rate Nyquist Theorem:
Ex. Find the maximum sampling interval for recording human voice (freq. range 300Hz – 3000Hz) t
sampling interval

31. Nyquist’s Sampling Theorem
See also: Wagon-wheel effect

32. Example
Calculate the minimum bit rate for recoding human voice, if each sample requires 60 levels of precision
(Human voice has range of 300Hz – 3000Hz)

33. Data Compression
Data compression refers to a technique that reduces the number of bits required to represent data
Lossy - some information is lost during compression (e.g, JPG, MP3)
Lossless - all information is retained in the compressed version (e.g., PNG, PCM)

34. Summary Data and signals Signal as series of sine waves Bandwidth
Fourier analysis
Bandwidth
Line coding
Analog to digital conversion
PCM
Data compression